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A particle moves along the curve y=7 x 2+4y=7 x 2+4 in such a way that its xx-coordinate is changing at a rate of −5−5 centimeters per second. At what rate is the particle's yy-coordinate changing when the particle is at the point where x=1x=1?

Respuesta :

Answer:

The y-coordinate is changing by the rate of -70 cm per sec.

Step-by-step explanation:

Given equation,

[tex]y = 7x^2 + 4[/tex]

Differentiating with respect to time (t),

[tex]\frac{dy}{dt}=14x \frac{dx}{dt}[/tex]

We have,

[tex]\frac{dx}{dt}=-5\text{ cm per sec}, x = 1[/tex]

[tex]\frac{dy}{dt} = 14(1)(-5)=-70\text{ cm per sec}[/tex]

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